Well-posedness for the 1D cubic nonlinear Schrödinger equation in Lp, p>2. (January 2023) - Hyakuna, Ryosuke
Abstract: In this paper, local well-posedness is shown for the one dimensional cubic nonlinear Schrödinger equation in L p -spaces for 2 < p < 4, which generalizes a classical result for p = 2 by Y. Tsutsumi in the direction opposite to the previous work for 1 < p < 2 by Y. Zhou. As a consequence, a local theory of solutions is developed for a class of data which decay more slowly than square integrable functions. Regularity properties of the local solutions in the L p -based Sobolev spaces and Stricharz spaces are also proved.